A166914 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 21, a(1) = 340.

21, 340, 5456, 87360, 1398016, 22369280, 357912576, 5726617600, 91625947136, 1466015416320, 23456247709696, 375299967549440, 6004799497568256, 96076792028200960, 1537228672719650816, 24595658764588154880

Offset: 0

Author

Klaus Brockhaus, Oct 27 2009

Keywords

• nonn

Comments

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+2) = 240*a(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (20,-64).

Crossrefs

Cf. A075153, A166912, A166913, A166915, A166916, A166917, A166927, A166965, A166984.

Programs

Magma

[Binomial(4^(n+3), 2)/96: n in [0..30]]; // G. C. Greubel, Oct 02 2024

Mathematica

CoefficientList[Series[(21-80x)/((1-4x)(1-16x)),{x,0,20}],x]  (* or *) LinearRecurrence[{20,-64},{21,340},20] (* Harvey P. Dale, Feb 23 2011 & Mar 30 2012 *)

PARI

{m=15; v=concat([21, 340], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]); v}

SageMath

A166914=BinaryRecurrenceSequence(20,-64,21,340)
[A166914(n) for n in range(31)] # G. C. Greubel, Oct 02 2024

Formula

a(n) = (64*16^n - 4^n)/3.

G.f.: (21 - 80*x)/((1-4*x)*(1-16*x)).

Limit_{n -> infinity} a(n)/a(n-1) = 16.

From G. C. Greubel, May 28 2016: (Start)

a(n) = 20*a(n-1) - 64*a(n-2).

E.g.f.: (1/3)*(-exp(4*x) + 64*exp(16*x)). (End)